A random matrix model for the density of states of jammed soft spheres with applied stress

Abstract

We investigate the addition of applied stress to a random block matrix model introduced by Parisi to study the Hessian matrix of soft spheres near the jamming point. In the infinite dimensional limit the applied stress translates the spectral distribution to the left, leading to a stability constraint. With negative stress, as in the case of a random network of stretched elastic springs, the spectral distribution is translated to the right, and the density of states has a peak before the plateau.